NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 21 



radiation is measured. We shall make use of that fact in the experi- 

 mental part of this paper, in order to calculate the maximum value 

 of the radiation of the atmosphere when the density of one of its 

 components approaches zero. 

 The relation 



represents the general expression for the radiation within the radia- 

 tion cone dQ, perpendicular to the unit of surface. Maurer bases his 

 computation of the atmosphere's radiation upon the more simple 

 expression 



J = -(i-e- aK ) 



a 



where he puts R equal to the height of the reduced atmosphere and 

 a equal to the absorption coefficient of unit volume. This is evidently 

 an approximation that is open to criticism. In the first place it is 

 not permissible to regard R as the height of the reduced atmosphere, 

 and this for two reasons : first, because the radiation is chiefly due to 

 the existence of water vapor and carbon dioxide in the atmosphere 

 vapors, whose density decreases rapidly with increase in the altitude ; 

 and, secondly, because we have here to deal with a radiation that 

 enters from all sides, R being variable with the zenith angle. But even 

 if we assign to R a mean value with regard to these conditions, 

 Maurer's formula will be true only for the case of one single emission 

 band and is, for more complicated cases, incapable of representing 

 the real conditions. I have referred to this case because it. shows 

 how extremely complicated are the conditions when all are taken into 

 consideration. 



If, with Maurer, we regard the atmosphere as homogeneous and 

 of uniform temperature, having a certain height, h, we must, con- 

 sidering that R is a function of the zenith angle, write ( i ) in the 

 following form: 



c/Q ( i — e~ ax ' E^*) cos 3> (7 



h 

 h 





where the integration is to be taken over the hemisphere represent- 

 ing the space. Now we have 



dQ, = d&dij/ sin <& 

 and therefore 



J x =S>l fdA 2 ( I _^x- c ^ F )sin$cos$^ (8) 



a x J o Jo 



